Families index theory for Overlap lattice Dirac operator. I

Details Families index theory for Overlap lattice Dirac operator. I Families index theory for Overlap lattice Dirac operator. I

2001-09-20

arxiv.org/abs/hep-lat/0109019v4

Nucl.Phys. B624 (2002) 469-484

Physics

High Energy Physics

High Energy Physics - Lattice

Latex, 23 pages. v4: minor improvements, results unchanged; to appear in Nucl.Phys.B

Scientific paper

10.1016/S0550-3213(01)00623-X

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over even-dimensional spheres in the orbit space. It reduces under suitable conditions to the topological charge of the usual (continuum) index bundle in the classical continuum limit (this is announced and sketched here; the details will be given in a forthcoming paper). Thus we see that topology of the index bundle of the Dirac operator over the gauge field orbit space can be captured in a finite-dimensional lattice setting.

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